{"ID":2854867,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.15101","arxiv_id":"2510.15101","title":"Operator Flow Matching for Timeseries Forecasting","abstract":"Forecasting high-dimensional, PDE-governed dynamics remains a core challenge for generative modeling. Existing autoregressive and diffusion-based approaches often suffer cumulative errors and discretisation artifacts that limit long, physically consistent forecasts. Flow matching offers a natural alternative, enabling efficient, deterministic sampling. We prove an upper bound on FNO approximation error and propose TempO, a latent flow matching model leveraging sparse conditioning with channel folding to efficiently process 3D spatiotemporal fields using time-conditioned Fourier layers to capture multi-scale modes with high fidelity. TempO outperforms state-of-the-art baselines across three benchmark PDE datasets, and spectral analysis further demonstrates superior recovery of multi-scale dynamics, while efficiency studies highlight its parameter- and memory-light design compared to attention-based or convolutional regressors.","short_abstract":"Forecasting high-dimensional, PDE-governed dynamics remains a core challenge for generative modeling. Existing autoregressive and diffusion-based approaches often suffer cumulative errors and discretisation artifacts that limit long, physically consistent forecasts. Flow matching offers a natural alternative, enabling...","url_abs":"https://arxiv.org/abs/2510.15101","url_pdf":"https://arxiv.org/pdf/2510.15101v1","authors":"[\"Yolanne Yi Ran Lee\",\"Kyriakos Flouris\"]","published":"2025-10-16T19:40:56Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[\"Diffusion Model\"]","has_code":false}